Greybody factor of scalar fields from black strings

TL;DR

This paper investigates the greybody factor for massless scalar fields in black string spacetimes, deriving analytical absorption probabilities in both coupled and uncoupled cases using wave equation solutions.

Contribution

It provides the first analytical expressions for scalar field greybody factors in black string backgrounds with and without Einstein tensor coupling.

Findings

Analytical absorption probability formulas derived for both cases.

Wave equation solutions expressed in hypergeometric and Bessel functions.

Matching solutions yields the low-energy absorption probability.

Abstract

The greybody factor of massless, uncharged scalar fields is studied in the background of cylindrically symmetric spacetimes, in the low-energy approximation. We discuss two cases. In the first case we derive analytical expression for the absorption probability when the spacetime is kinetically coupled with the Einstein tensor. In the second case we do the analysis in the absence of the coupling constant. For this purpose we analyze the wave equation which is obtained from Klein-Gordon equation. The radial part of the wave equation is solved in the form of the hypergeometric function in the near horizon region, whereas in the far region the solution is of the form of Bessel's function. Finally, considering continuity of the wave function we smoothly match the two solutions in the low energy approximation to get the formula for the absorption probability.